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GEOMETRY, FUR2 2006 VCAA 2

An allotment of land contains a communications tower, `PQ`.

Points `S`, `Q` and `T` are situated on level ground.

From `S` the angle of elevation of `P` is 20°.

Distance `SQ` is 125 metres.

Distance `TQ` is 98 metres. 
 

Geometry and Trig, FUR2 2006 VCAA 2
 

  1. Determine the height, `PQ`, of the communications tower.

     

    Write your answer, in metres, correct to one decimal place.  (1 mark)

  2. Determine the angle of depression of `T` from `P`.

     

    Write your answer, in degrees, correct to one decimal place.  (1 mark) 

Show Answers Only
  1. `45.5\ text{m (1 d.p.)}`
  2. `24.9^@\ text{(1 d.p.)}`
Show Worked Solution

a.   `text(In)\ Delta PQS,`

♦ Mean mark of both parts (combined) was 50%.
`tan 20^@` `= (PQ)/125`
`:. PQ` `= 125 xx tan 20^@`
  `= 45.49…`
  `= 45.5\ text{m (1 d.p.)}`

 

b.     

 

`theta = text(angle of depression of)\ T\ text(from)\ P`

`tan theta` `= 45.5/98`
  `= 0.464…`
`:. theta` `= 24.90…`
  `= 24.9^@\ text{(1 d.p.)}`

 

GEOMETRY, FUR1 2011 VCAA 2 MC


 

The point `Q` on building `B` is visible from the point `P` on building `A`, as shown in the diagram above.

Building `A` is 16 metres taller than building `B`.

The horizontal distance between point `P` and point `Q` is 23 metres.

The angle of depression of point `Q` from point `P` is closest to

A.    `35°`

B.    `41°`

C.    `44°`

D.    `46°`

E.    `55°`

Show Answers Only

`A`

Show Worked Solution

`tan theta` `= 16/23`
`theta` `= 34.8^@`

 

`:.\ text(Angle of depression from)\ P\ text(to)\ Q = 34.8^@`

`text{(alternate,}\ PS\ text(||)\ RQ text{)}`

`=> A`